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This paper presents a novel and efficient framework to the active map-based global localization problem for mobile robots operating in large and cooperative environments. The paper proposes a rational criteria to select the action that minimizes the expected number of remaining position hypotheses, for the single robot case and for the cooperative case, where the lost robot takes advantage of observations coming from a sensor network deployed on the environment or from other localized robots. Efficiency in time complexity is achieved thanks to reasoning in terms of the number of hypotheses instead of in terms of the belief function. Simulation results in a real outdoor environment of 10.000 m2 are presented validating the presented approach and showing different behaviours for the single robot case and for the cooperative one.